### Functions

### Lesson 1: Introduction

A function consists of four main components: Existence, Domain, Rule and Range

A function consists of four main components: Existence, Domain, Rule and Range

(1) Existence

Let f be a relationship that maps a set of values, X to another set of values, Y. f is a function if every value of x is mapped to exactly 1 value of y.

Not a function

A function

The domain of a function f, denoted by , is the set of input values usually represented as x.

(2) Domain, Rule and Range

The rule of a function f, denoted by f (x), is the equation that describes the relationship that maps the domain to the range.

The range of a function f, denoted by , is the set of y values generated by its rule y = f (x), and domain, . It can be obtained by looking at the set of y values from the graph of f.

Example 1

Example 2

(3) Notation

Here are two examples on how we can write a function f as follows:

Rule

Domain